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A Pendant for Polya: The One-Loop Partition Function of N=4 SYM on R x S^3

Marcus Spradlin·Anastasia Volovich
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Abstract

We study weakly coupled SU(N) N = 4 super Yang-Mills theory on R x S^3 at infinite N, which has interesting thermodynamics, including a Hagedorn transition, even at zero Yang-Mills coupling. We calculate the exact one-loop partition function below the Hagedorn temperature. Our calculation employs the representation of the one-loop dilatation operator as a spin chain Hamiltonian acting on neighboring sites and a generalization of Polya's counting of `necklaces' (gauge-invariant operators) to include necklaces with a `pendant' (an operator which acts on neighboring beads). We find that the one-loop correction to the Hagedorn temperature is delta ln T_H = + lambda/8 pi^2.

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Marcus Spradlin, Anastasia Volovich. 2004-09-20. A Pendant for Polya: The One-Loop Partition Function of N=4 SYM on R x S^3. https://doi.org/10.1016/j.nuclphysb.2005.01.007

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